Optical-Pumping Transients in Rubidium-87 and Application to Excited-State Disorientation Cross Sections

Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical-pumping process, both with and without buffer gas present. The observed transients are single exponentials with no buffer gas present, and double exponentials with buffer gas present, over a wide range of pumping intensities and relaxation times. These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin is included and a single relaxation time is assumed. From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section ${\sigma }_{\mathrm{eff}}$ is deduced for the disorientation of rubidium-87 within the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state as a result of its collision with a buffer-gas atom. It is shown that ${\sigma }_{\mathrm{eff}}={\sigma }_{\frac{1}{2}}+{\sigma }_{\frac{3}{2}}$, where ${\sigma }_{\frac{1}{2}}$ is the cross section for disorientation within the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ level, and ${\sigma }_{\frac{3}{2}}$ is the cross section for transfer from the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ level to the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ level by means of collisions with the buffer gas. On the basis of recently measured values for ${\sigma }_{\frac{3}{2}}$, values are deduced for ${\sigma }_{\frac{1}{2}}$. The cross sections are: ${\sigma }_{\frac{1}{2}}(\mathrm{R}\mathrm{b}-\mathrm{H}\mathrm{e})=1.5\mathrm{}\left(0.8\right)\mathrm{}\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$, ${\sigma }_{\frac{1}{2}}(\mathrm{R}\mathrm{b}-\mathrm{N}\mathrm{e})=4.4\mathrm{}\left(2.2\right)\mathrm{}\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$, and ${\sigma }_{\frac{1}{2}}(\mathrm{R}\mathrm{b}-\mathrm{A}\mathrm{r})=3.5\mathrm{}\left(1.8\right)\mathrm{}\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. These cross sections are deduced from a model in which the probabilities for ${\mathrm{Rb}}^{87}$ to relax from any hyperfine level to any other are all equal. This model gives a better fit with the observed transients than the assumption that the electron spin only is randomized in the $P_{\frac{1}{2}}$ state with the nuclear spin unaffected. We show that accurate relaxation-time measurements can be made by measuring the time constants associated with the double exponentials as a function of light intensity, and extrapolating them to zero light intensity. Moreover, since no shutter is required, relaxation times <${10}^{-3\mathrm{}}$ sec can be easily observed.